1. Ruby Flyer is a UD student who makes cupcakes in her spare time. She is famous for making 2 types of cupcakes: Nilla Sprinkles (vanilla) and Midnight Magic (chocolate). Both types require eggs in their recipes and Ruby just purchased 240 organic eggs from a local farm. According to the recipes, 3 eggs are required to make 1 dozen of Nilla Sprinkles cupcakes and 2 eggs are required to make 1 dozen of Midnight Magic cupcakes. Ruby only has enough wrappers to make at most 75 dozen cupcakes. Ruby sells Nilla Sprinkles for $25 per dozen and Midnight Magic for $20 per dozen. Ruby wants to know how many dozens of Nilla Sprinkles and Midnight Magic cupcakes should be made in order to make as much money as possible. Let x = number of Nilla Sprinkles cupcakes to make for the week (in dozens) x2 = number of Midnight Magic cupcakes to make for the week (in dozens) a) Write the objective function for this problem. (You don't need to write the full model here, just the objective function) b) Write the constraint that makes sure we do not exceed the available supply of eggs. (You don't need to write the full model here, just the single constraint) Write the constraint that makes sure we do not exceed the total amount of cupcakes Ruby can make in a week. (You don't need to write the full model here, just the single constraint) c)
1. Ruby Flyer is a UD student who makes cupcakes in her spare time. She is famous for making 2 types of cupcakes: Nilla Sprinkles (vanilla) and Midnight Magic (chocolate). Both types require eggs in their recipes and Ruby just purchased 240 organic eggs from a local farm. According to the recipes, 3 eggs are required to make 1 dozen of Nilla Sprinkles cupcakes and 2 eggs are required to make 1 dozen of Midnight Magic cupcakes. Ruby only has enough wrappers to make at most 75 dozen cupcakes. Ruby sells Nilla Sprinkles for $25 per dozen and Midnight Magic for $20 per dozen. Ruby wants to know how many dozens of Nilla Sprinkles and Midnight Magic cupcakes should be made in order to make as much money as possible. Let x = number of Nilla Sprinkles cupcakes to make for the week (in dozens) x2 = number of Midnight Magic cupcakes to make for the week (in dozens) a) Write the objective function for this problem. (You don't need to write the full model here, just the objective function) b) Write the constraint that makes sure we do not exceed the available supply of eggs. (You don't need to write the full model here, just the single constraint) Write the constraint that makes sure we do not exceed the total amount of cupcakes Ruby can make in a week. (You don't need to write the full model here, just the single constraint) c)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Ruby Flyer is a UD student who makes cupcakes in her spare time. She is famous for making 2 types
of cupcakes: Nilla Sprinkles (vanilla) and Midnight Magic (chocolate). Both types require eggs in their
recipes and Ruby just purchased 240 organic eggs from a local farm. According to the recipes,
3 eggs are required to make 1 dozen of Nilla Sprinkles cupcakes and 2 eggs are required to make 1
dozen of Midnight Magic cupcakes. Ruby only has enough wrappers to make at most 75 dozen
cupcakes. Ruby sells Nilla Sprinkles for S25 per dozen and Midnight Magic for $20 per dozen. Ruby
wants to know how many dozens of Nilla Sprinkles and Midnight Magic cupcakes should be made in
order to make as much money as possible.
Let x = number of Nilla Sprinkles cupcakes to make for the week (in dozens)
x2 = number of Midnight Magic cupcakes to make for the week (in dozens)
a)
Write the objective function for this problem. (You don't need to write the full model
here, just the objective function)
b)
Write the constraint that makes sure we do not exceed the available supply of eggs.
(You don't need to write the full model here, just the single constraint)
Write the constraint that makes sure we do not exceed the total amount of cupcakes
Ruby can make in a week. (You don't need to write the full model here, just the single constraint)
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